Sympathetic Ground State Cooling and Time-Dilation Shifts in an ^{27}Al^{+} Optical Clock.

Area of Science:

• Quantum Information Science
• Atomic, Molecular, and Optical (AMO) Physics
• Precision Measurement

Background:

• Sympathetic cooling is crucial for preparing ions in their motional ground states for quantum applications.
• Previous sympathetic cooling methods faced limitations in achieving high fidelity and reducing systematic uncertainties.
• Precise control over ion motion is essential for advanced atomic clocks and quantum simulations.

Purpose of the Study:

• To report on Raman sideband cooling of magnesium-25 ions ({}^{25}Mg^{+}) to sympathetically cool aluminum-27 ions ({}^{27}Al^{+}).
• To investigate the cooling process and identify factors limiting the efficiency of three-dimensional (3D) ground-state cooling.
• To characterize residual energies and heating rates, and to estimate the secular motion time-dilation shift.

Main Methods:

• Raman sideband cooling of ^{25}Mg^{+} ions.
• Sympathetic cooling of a ^{25}Mg^{+}-^{27}Al^{+} two-ion system.
• Rate-equation simulations to study Fock-state distribution evolution.
• Characterization of secular motion modes, residual energies, and heating rates.

Main Results:

• Achieved near three-dimensional (3D) ground-state cooling of the secular modes of motion in the two-ion pair.
• Identified and discussed heating sources that affect the efficiency of 3D sideband cooling.
• Estimated a secular motion time-dilation shift of -(1.9±0.1)×10^{-18} for an ^{27}Al^{+} clock.

Conclusions:

• Raman sideband cooling provides an effective method for sympathetic ground-state cooling of ion qubits.
• The achieved reduction in time-dilation shift uncertainty represents a significant improvement for ^{27}Al^{+} atomic clocks.
• This work paves the way for more precise quantum measurements and enhanced atomic clock performance.